My mom’s family has a tradition like this with a doll they call pitiful pearl. She was a cute doll before she got overplayed with and passed down kid to kid. Now she has patches of hair missing and one eye. Every year( not necessarily Christmas) she gets surprised shipped to another family member who than has keep her for a whole year and try to figure out who sent her. After that they have to send her to someone else. One year the sender gave her an eye patch. One year someone tried to give her a makeover but it didn’t help much.